Statistics

In this course, students are taught the foundational concepts of major stochastic fields and associated topics, including Statistics, probability, and combinatorics. The course is presented in “flipped-classroom” format, such that students are expected to learn concepts on their own, and then practice application in the classroom.

The course introduces the student to the statistical analysis of time series data and simple time series models, and showcases what time series analysis can be useful for. Topics include autocorrelation; stationarity, trend removal and seasonal adjustment; AR, MA, ARMA, ARIMA; estimation; forecasting; unit root test; introduction to financial time series and the ARCH/GARCH models; basic spectral analysis. The use of R for time series analysis is covered.

Information is a fundamental concept in the world around us that can be investigated from several perspectives. The mathematical theory of information provides a framework for a formal description and interpretation of information. In many ways, this mathematical framework (its applications and the interpretations it provides) is based on concepts from probability theory and statistics. This course provides students with an introduction to the field of information theory. Students will learn to apply and interpret a wide range of concepts from statistics and probability theory to develop, model, and understand the concept of information, as well as related ideas, in a structured and organized way. Many of the tools of statistics and probability theory students encounter in the course should be familiar to them from introductory or intermediate statistics courses, while other concepts might be new.

This course covers statistical inference in one population, key concepts in hypothesis testing, issues of comparing two populations, concepts of the simple linear regression model, and use of statistical software to perform analyses. Prerequisite: introductory course in statistics.

This course introduces students to the statistical computing and programming, with the main focus on R, Python, and SAS. Students learn basic computing and programming concepts including scripting, variables, expressions, assignments, control structures, and data structures. On the statistical side, they will learn to load raw data, make numerical and graphical summaries of data, and conduct various estimation and testing procedures. Topics include descriptive statistics, statistical estimation, robust estimation, categorical data analysis, testing hypotheses, ANOVA, regression analysis, performing resampling methods and simulations. Some basic knowledge of R is assumed.

This course is part of the LM degree program and so is intended for advanced level students. Enrollment is by consent of the instructor. This course discusses fundamentals of the most important multivariate techniques that help to make intelligent use of large data base by recognizing patterns for predicting or estimating an output based on one or more inputs. At the end of the course the student is able; to represent and organize knowledge about big data collections; to turn data into actionable knowledge; and to choose the best suited methodology for the problem at hand to critically interpret the results. The course discusses topics including an introduction to supervised statistical learning; resampling methods: Cross-Validation, and Bootstrap; classification: Naive Bayes, k-Nearest Neighbors, Logistic Regression, and Linear Discriminant Analysis; Dimension Reduction and Regularization; Tree-based methods: Regression and Classification trees, Bagging, Random Forests, and Boosting; and an overview of the main machine learning methods: Support Vector Machines, and Neural Networks.